In the case of travel expenses - yes you can. In the case of other expenses - probably not.

The general rule is that the expense
has to be necessary and if you could have claimed reimbursement
then it was not necessary for you to incur the expense. However, in
the case of travel expenses the allowance being claimed is at a
rate per mile - this is Mileage Allowance Relief (MAR)
and is granted by law in respect of qualifying journeys. So if the
journey qualifies then MAR is due at the statutory rate less any
reimbursement. As long as the journey is necessary then MAR is
due.